“Hinn” is the form of the definite article (the “the”) that you add to the end of masculine nouns, while “hið” is the form you add to neuter nouns. You cannot know for sure which gender a word belongs to just by looking at it, instead you slowly learn it by seeing how the word affects other words in the sentence and how its definite article changes.
Lets take two examples:
- “Hús” is a neuter noun. We add “hið” to the end of it and we get “hús + hið”. We don’t care about the “h” and we’re left with “húsið” (the house).
- “Kaffi” is also a neuter noun. To add a definite article to it, we create “kaffi + hið”. We don’t care about the “h” and so we’re left with “kaffi + ið”. The vowel in the noun is much more important than the vowel in the definite article, so we’re left with “kaffi + ð”. The result is “kaffið” (the coffee).